Problem 3: Consider the following message signal, channel filter, modulator, and demodulator. A x(t) cos(2000nt) X(f) channel filter r(t) z(t) H(f) ILPF 0 100 f cutoff=100 cos(2πfet) |H(f)| 900 1000 1100 y(t) 1 a) Carefully sketch the Fourier transforms of r(t), z(t), and y(t) assuming the receiver local oscillator is f. = 1000 Hz. Be sure to label the frequency and amplitude axes carefully. b) Notice that for f. =1000, y(t) = x(t) because of the channel filter distortion. Assuming the transmitter oscillator remains at 1000 Hz, find value for f, and A such that y(t) = x(t) for this particular message signal.
Problem 3: Consider the following message signal, channel filter, modulator, and demodulator. A x(t) cos(2000nt) X(f) channel filter r(t) z(t) H(f) ILPF 0 100 f cutoff=100 cos(2πfet) |H(f)| 900 1000 1100 y(t) 1 a) Carefully sketch the Fourier transforms of r(t), z(t), and y(t) assuming the receiver local oscillator is f. = 1000 Hz. Be sure to label the frequency and amplitude axes carefully. b) Notice that for f. =1000, y(t) = x(t) because of the channel filter distortion. Assuming the transmitter oscillator remains at 1000 Hz, find value for f, and A such that y(t) = x(t) for this particular message signal.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![Problem 3: Consider the following message signal, channel filter, modulator, and demodulator.
A
x(t)
cos(2000nt)
X(f)
channel filter
r(t)
z(t)
H(f)
ILPF
0
100 f
cutoff=100
cos(2πfet)
|H(f)|
900 1000 1100
y(t)
1
a) Carefully sketch the Fourier transforms of r(t), z(t), and y(t) assuming the receiver local
oscillator is f. = 1000 Hz. Be sure to label the frequency and amplitude axes carefully.
b) Notice that for f. =1000, y(t) = x(t) because of the channel filter distortion. Assuming
the transmitter oscillator remains at 1000 Hz, find value for f, and A such that y(t) = x(t)
for this particular message signal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2a1896c-46fc-46db-a11f-1831b712b13c%2F9ba3b66b-166a-4a08-b372-4533324ce2e9%2Fmkpdnh7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3: Consider the following message signal, channel filter, modulator, and demodulator.
A
x(t)
cos(2000nt)
X(f)
channel filter
r(t)
z(t)
H(f)
ILPF
0
100 f
cutoff=100
cos(2πfet)
|H(f)|
900 1000 1100
y(t)
1
a) Carefully sketch the Fourier transforms of r(t), z(t), and y(t) assuming the receiver local
oscillator is f. = 1000 Hz. Be sure to label the frequency and amplitude axes carefully.
b) Notice that for f. =1000, y(t) = x(t) because of the channel filter distortion. Assuming
the transmitter oscillator remains at 1000 Hz, find value for f, and A such that y(t) = x(t)
for this particular message signal.
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